You will have to share the base/workspace with the third party you are wanting to give API access to.

After that the third party can create an API key via their own account and they will then have access to only the bases/workspaces you have given them access to and not all your bases

@Jan_Poboril - youd have to create another user that has access to just what you want to share and the permission level you want to give then use the API key of that user